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Any flow is an orbit factor of any flow

Published online by Cambridge University Press:  19 September 2008

Donald Ornstein  and
Benjamin Weiss
Donald Ornstein
Affiliation:
Department of Mathematics, Stanford University, Stanford CA 94305, USA
Benjamin Weiss
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel
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Abstract

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We prove that given any two ergodic non-singular flows , St, the first can be time changed to t so that St is a factor of t. A corresponding result for transformations is that if , T are any two ergodic non-singular transformations then there is a tower over that has T as a factor.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 1 , March 1984 , pp. 105 - 116
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Arnoux, P., Ornstejn, D. S. & Weiss, B.. Cutting and stacking, interval exchanges and geometric models. Israel J. Math. To appear.Google Scholar
[2]Connes, A., Feldman, J. & Weiss, B.. Amenable equivalent relations are generated by a single transformation. Ergod. Th. & Dynam. Sys. 1 (1981), 431–450.CrossRefGoogle Scholar
[3]Kakutani, S.. Induced measure preserving transformation. Proc. Japan Acad. 19 (1943), 635–641.Google Scholar
[4]Krieger, W.. On ergodic flows and isomorphism of factors. Math Ann. 223 (1976), 19–70.CrossRefGoogle Scholar
[5]Ornstein, D., Rudolph, D. & Weiss, B.. Equivalence and non equivalence theory. Memoirs Amer. Math. Soc. 262 (1982).Google Scholar
[6]Rudolph, D.. Smooth orbit equivalence of ergodic Rd-actions, d≥2. Trans. Amer. Math. Soc. 253 (1979), 291–302.Google Scholar
[7]Weiss, B.. Orbit equivalence of non-singular actions. In Theorie Ergodique, Monog. 29, Enseign. Math. 1981, pp. 77–107.Google Scholar